How To Get Annotation For Bed File From Another Bed File

Hello All,

I have a bed file (with Chr, Start, End, Name, Score and Strand)

Chr1 5678 5680 NA 7  +
Chr1 700  800  NA 8  -
Chr1 900  1200 NA 10 -

and would like to know, how can I get the annotation for the name column from another bed file

Chr1 5500 6000 Gene1 x +
Chr1  500 1000 Gene2 x -

or any standard genome file formats like gbk or .fna files or for that matter another bed file? So mu output file will be a bed file with Chr, Start, End, Name and Strand.

Chr1 5678 5680 Gene1 7 +
Chr1 700  800  Gene2 8 -
Chr1 900  1200 Gene2 10 -

Any easy and standard way to do this??

Bedtools usually operates more on the features but not sure if annotation from one bedfile can be extracted into the other based on overlapping feaures.

Thanks in advance!